Abstract
Simultaneous equations for the BCS parameter and for the Fermi energy in the BCS state are studied at low carrier concentrations in bulk and thin-film superconducting semiconductors at for large cutoff energies, and solutions are plotted in the form of universal curves. For electron-electron attraction greater than some critical value in bulk material or for any attractive interaction in very thin films, the pair-binding energy tends to a constant limit for low , and pairing without superconductivity is expected in some temperature range. Solutions of simultaneous equations for as obtained by formal application of the BCS theory, and for the Fermi energy at , are also obtained in bulk material; but it is shown that at low carrier concentrations the temperature at which pairing takes place is given by , while it is thought that superconductivity will not set in until a lower temperature, of the order of the Bose-Einstein condensation temperature of the pairs, is reached. By combining the above theory with a previously published model for superconductivity in Zr-doped SrTi, predictions for this material in the region of low carrier concentrations are made.
- Received 14 May 1969
DOI:https://doi.org/10.1103/PhysRev.186.456
©1969 American Physical Society